Question

question
solve for x.

Explanation:

Step1: Apply the intersecting chords theorem

When two chords intersect in a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs. So, \(75^{\circ}=\frac{1}{2}[(6 + 9x)+(18x + 9)]\).

Step2: Simplify the equation

Multiply both sides by 2: \(150=(6 + 9x)+(18x + 9)\).
Combine like - terms: \(150 = 27x+15\).

Step3: Solve for \(x\)

Subtract 15 from both sides: \(150 - 15=27x\), so \(135 = 27x\).
Divide both sides by 27: \(x=\frac{135}{27}\).

Answer:

\(x = 5\)